A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude of oscillation is 40 cm . What should be the least period of these oscillations, so that the object is not detached from the platform? [Take $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

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Aicharya · Accepted Answer

From the diagram, $\mathrm{mg} \div \mathrm{N}=\mathrm{ma}$
For the object to just lose the Contact with the surface, $\begin{array}{ll} & N=0 \\ \therefore \quad & m g=m a \\ \therefore \quad & g=a \\ \therefore \quad & g=A \omega^2 \end{array}$

$\begin{aligned} & \therefore \quad \omega=\sqrt{\frac{g}{A}}=\sqrt{\frac{10}{0.4}}=\sqrt{\frac{100}{4}}=\frac{10}{2}=5 \\ & \therefore \quad \frac{2 \pi}{T}=5 \\ & \therefore \quad T=\frac{2 \pi}{5}=0.4 \pi\end{aligned}$

A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction.…

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